Discontinuous Galerkin Methods for Friedrichs’ Systems. Part II. Second‐order Elliptic PDEs

SIAM Journal on Numerical Analysis ◽

10.1137/05063831x ◽

2006 ◽

Vol 44 (6) ◽

pp. 2363-2388 ◽

Author(s):

Alexandre Ern ◽

Jean‐Luc Guermond

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Elliptic Pdes ◽

Galerkin Methods ◽

Friedrichs Systems

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Interior Penalty Discontinuous Galerkin Methods for Second Order Linear Non-divergence Form Elliptic PDEs

Journal of Scientific Computing ◽

10.1007/s10915-017-0519-3 ◽

2017 ◽

Vol 74 (3) ◽

pp. 1651-1676 ◽

Author(s):

Xiaobing Feng ◽

Michael Neilan ◽

Stefan Schnake

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Divergence Form ◽

Second Order ◽

Elliptic Pdes ◽

Galerkin Methods ◽

Interior Penalty ◽

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Abstract theory of hybridizable discontinuous Galerkin methods for second-order quasilinear elliptic problems

Computational Mathematics and Mathematical Physics ◽

10.1134/s096554251403004x ◽

2014 ◽

Vol 54 (3) ◽

pp. 474-490 ◽

Author(s):

R. Z. Dautov ◽

E. M. Fedotov

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Abstract Theory ◽

Hybridizable Discontinuous Galerkin ◽

Hybridizable Discontinuous Galerkin Methods ◽

Quasilinear Elliptic Problems ◽

Quasilinear Elliptic

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Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation

Applicable Analysis ◽

10.1080/00036811.2019.1636968 ◽

2019 ◽

pp. 1-15 ◽

Author(s):

Limin He ◽

Weimin Han ◽

Fei Wang ◽

Wentao Cai

Keyword(s):

Wave Equation ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Unconditional Stability ◽

Second Order ◽

Optimal Error Estimates ◽

Galerkin Methods ◽

Optimal Error ◽

Second Order Wave Equation

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Performance of Discontinuous Galerkin Methods for Elliptic PDEs

SIAM Journal on Scientific Computing ◽

10.1137/s1064827501388339 ◽

2002 ◽

Vol 24 (2) ◽

pp. 524-547 ◽

Author(s):

Paul Castillo

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Pdes ◽

Galerkin Methods

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Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142903421527 ◽

2004 ◽

Vol 42 (3) ◽

pp. 1146-1166 ◽

Author(s):

Zhangxin Chen ◽

Hongsen Chen

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Pointwise Error ◽

Pointwise Error Estimates ◽

Second Order Elliptic Problems

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Nonstandard Local Discontinuous Galerkin Methods for Fully Nonlinear Second Order Elliptic and Parabolic Equations in High Dimensions

Journal of Scientific Computing ◽

10.1007/s10915-018-0765-z ◽

2018 ◽

Vol 77 (3) ◽

pp. 1534-1565

Author(s):

Xiaobing Feng ◽

Thomas Lewis

Keyword(s):

Discontinuous Galerkin ◽

Parabolic Equations ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Galerkin Methods ◽

High Dimensions ◽

Fully Nonlinear ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Elliptic And Parabolic Equations

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Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media

Journal of Computational Physics ◽

10.1016/j.jcp.2014.04.009 ◽

2014 ◽

Vol 272 ◽

pp. 88-107 ◽

Author(s):

Ching-Shan Chou ◽

Chi-Wang Shu ◽

Yulong Xing

Keyword(s):

Wave Equation ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Heterogeneous Media ◽

Second Order ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Energy Conserving ◽

Second Order Wave Equation

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Discontinuous Galerkin Methods for Friedrichs’ Systems

Numerical Mathematics and Advanced Applications ◽

10.1007/978-3-540-34288-5_5 ◽

2007 ◽

pp. 79-96

Author(s):

Alexandre Ern ◽

Jean-Luc Guermond

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Friedrichs Systems

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Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems

SIAM Journal on Numerical Analysis ◽

10.1137/070685105 ◽

2009 ◽

Vol 47 (1) ◽

pp. 508-533 ◽

Author(s):

E. Burman ◽

B. Stamm

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Elliptic Problems ◽

Second Order ◽

Galerkin Methods ◽

Second Order Elliptic Problems ◽

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A posteriorierror estimates for discontinuous Galerkin methods using non-polynomial basis functions Part I: Second order linear PDE

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2015069 ◽

2016 ◽

Vol 50 (4) ◽

pp. 1193-1222 ◽

Author(s):

Lin Lin ◽

Benjamin Stamm

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Second Order ◽

Basis Functions ◽

Polynomial Basis ◽

Galerkin Methods ◽

Order Linear ◽

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